Negative refractive index in dielectric crystals containing stoichiometric rare-earth ions

TL;DR

This paper explores the potential for negative refractive index in dielectric crystals with rare-earth ions, identifying Erbium crystals as promising candidates through theoretical analysis and initial optical measurements.

Contribution

It derives conditions for negative permittivity and permeability in such crystals and highlights Erbium crystals as suitable materials based on experimental linewidth data.

Findings

${}^7\mathrm{LiF}$ satisfies the criteria for negative permeability.

Erbium crystals are identified as promising for negative refractive index.

Initial optical measurements support the theoretical predictions.

Abstract

We investigate the prospect of achieving negative permittivity and permeability at optical frequencies in a dielectric crystal containing stoichiometric rare-earth ions. We derive the necessary transition linewidth, ion density and electric and magnetic oscillator strengths using a simplified model of non-interacting dipoles. We identify Erbium crystals in a magnetically ordered phase as the most promising material to meet these conditions, and describe initial optical measurements of two potential candidates, \ercl{} and ${}^7$\lierf{}, which display linewidths of 3~GHz and 250~MHz, respectively. The properties of ${}^7$\lierf{} satisfied our criterion for negative permeability.